Stabilization of valence fluctuations in the cerium solid by the time-dependent collision approach

The collision-generated hybridization which has been found responsible for the on-site mixing of the atomic-likef-state and the band-liked states in mixed valence solids has been studied for the cerium solid. A practical expression which depends on the lattice constant and temperature has been obtained for the collision-generated hybridization. Numerical calculations show that the valence varies continuously with lattice constant and that temperature makes the transition smoother. The collision-generated hybridization is found to be of significant strength in the intermediate valence regime; but over a wide range of the valence near 3.5 it varies rather slowly without preferring a particular valence. Factors which can assist the collision-generated hybridization in stabilizing the mixed valence phase at a particular lattice constant are discussed.     

Nuclear and atomic models

A theorem concerning fermion interaction is postulated and applied to the problems of atomic (electronic) and nuclear physics. Model building basedsolely upon the postulate thatadjacent like fermions must be singlet paired accounts for the closed shells ofboth nuclear and atomic structure. The implied antiferromagnetic FCC lattice of protons and neutrons in alternating layers has been found previously to be the lowest-energy solid configuration of nuclear matter (N=P) (Canuto and Chitre, 1974). The buildup of the FCC lattice from a central tetrahedron reproduces all of the shells and subshells of the isotropic harmonic oscillator, which of course is the basis for the shell model. In atomic structure, the singlet pairing of adjacent electrons implies closed-shell structures uniquely at the six noble gases and the three noble metals, Ni, Pd, and Pt. The basis for the postulate concerning fermions is found in terms of classical electrodynamics; it is a microscopic corollary of Biot-Savart's law that parallel currents attract whereas antiparallel currents repel.     

Dynamic and thermodynamic consequences of adsorbate lateral interactions in surface reaction kinetics

The effects of lateral interactions on the two-dimensional distribution of adspecies on solid surfaces and their consequences for reaction kinetics are demonstrated for the bimolecular reactive systemA+BAB. The discussion concentrates on systems where one reactant,A, is stationary while the other,B, is freely diffusing and instantaneously relaxing. A modified Bethe-Peierls-type lattice gas approximation is formulated in order to account for the rapidly-equilibrating distribution ofB atoms. The approximation takes into account all nearest and next nearest neighbor interactions between the adspecies and the nonuniformity of the lattice available toB implied by the presence of immobileA's on the surface. This model is combined with a Monte Carlo simulation of the reactive events in order to calculate reaction rates, e.g., in temperature-programmed processes. The rates are compared with full Monte Carlo simulations (for all kinetic processes), showing good agreement between the two schemes, except at very high coverages, where very long range correlations in the system which are ignored in the lattice gas approximation must be taken into account.This paper is dedicated to Howard Reiss in celebration of his 66th birthday.     

New scattering formula for the analysis of X-ray line broadening by composition profiles

The variation of the lattice constantsa _i (i=1,2,3) with the depthR in a crystalline solid leads to broadening of the x-ray reflections. The broadening is calculated for polycrystalline samples, where the lattice constant profilea _i (R) extends over several grain diameters. The calculation is performed by superimposing, in kinematical theory, the waves scattered from the lattice planes with varying distances and taking into account the absorption of the x-rays in the material.     

Concentration dependence of the lattice constant of disordered interstitial solid solutions

The lattice constant of the A-(C) interstitial solid solutions is calculated, and its dependence on the solution composition is determined for arbitrary concentration c_C of the C atoms and their arbitrary distribution over interstices of different types. For c _c ≪1, a linear dependence of the lattice constant on c_C is established, which is also observed experimentally. The influence of temperature redistribution of interstitial atoms over interstices of different types, leading to a specific nonlinear temperature dependence of the lattice constant, is investigated. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 3–5, December, 2005.     

Super-Instantons, Perfect Actions, Finite-Size Scaling, and the Continuum Limit

We discuss some aspects of the continuum limit of some lattice models, in particular the 2DO(N) models. The continuum limit is taken either in an infinitevolume or in a box whose size is a fixed fraction of the infinite-volume correlation length. We point out that in this limit the fluctuations of the lattice variables must be O(1) and thus restore the symmetry which may have been broken by the boundary conditions (b.c.). This is true in particular for the socalled super-instanton b.c. introduced earlier by us. This observation leads to a criterion to assess how close a certain lattice simulation is to the continuum limit and can be applied to uncover the true lattice artefacts, present even in the so-called “perfect actions”. It also shows that David’s recent claim that superinstanton b.c. require a different renormalization must either be incorrect or an artefact of perturbation theory.     

The zero-point energy in the molecular hydrogen crystal

We propose a modified Einstein approximation to describe zero-point energy vibrations in a quantum crystal. Our aim was to develop a computationally cheap tool suitable for lattice structure optimisation. As in the classical Einstein model the representative atom vibrates in an effective potential due to the surrounding atoms of the crystal; the atoms however are not strictly placed at the positions corresponding to the crystal potential energy minima but their positions are described by the quantum mechanical density distributions. The effective potential computed that way is suitable for the application in solid para-hydrogen in contrast to the normal (unmodified) Einstein approximation. We compute the cohesive energy of the para-hydrogen crystal and perform lattice structure optimisation. The hexagonal closed packed is more stable than the fcc closed packed lattice and the lattice constants obtained are in very good agreement with the experimental values.     

Effect of a lattice upon an interacting system of electrons in two dimensions: Breakdown of scaling and decay of persistent currents

The ground state of an electron gas is characterized by the interparticle spacing to the effective Bohr radius ratio r _s = a/a _B ^*. For polarized electrons on a two dimensional square lattice with Coulomb repulsion, we study the threshold value r _s ^* below which the lattice spacing s becomes a relevant scale and r _s ceases to be the scaling parameter. For systems of small ratios s/a _B ^*, s becomes only relevant at small r _s (large densities) where one has a quantum fluid with a deformed Fermi surface. For systems of large s/a _B ^*, s plays also a role at large r _s (small densities) where one has a Wigner solid, the lattice limiting its harmonic vibrations. The thermodynamic limit of physical systems of different a _B ^* is qualitatively discussed, before quantitatively studying the lattice effects occurring at large r _s . Using a few particle system, we compare exact numerical results obtained with a lattice and analytical perturbative expansions obtained in the continuum limit. Three criteria giving similar values for the lattice threshold r _s ^* are proposed. The first one is a delocalization criterion in the Fock basis of lattice site orbitals. The second one uses the persistent current which can depend on the interaction in a lattice, while it becomes independent of the interaction in the continuum limit. The third one takes into account the limit imposed by the lattice to the harmonic vibrations of the electron solid.Received: 20 January 2004, Published online: 18 June 2004PACS: 71.10.-w Theories and models of many-electron systems - 71.10.Fd Lattice fermion models (Hubbard model, etc.) - 73.20.Qt Electron solids     

Coupling of orientational and translational modes in solid C60 and C70

The orientational phase transitions in solid C₆₀ and C₇₀ are accompanied by quite different anomalies in the crystalline strains. In solid C₆₀ the phase transition Fm3m→Pa3 is primarily an orientational effect (antiferro-rotational), which is driven by the condensation of orientational modes belonging to X₅ ⁺ irreducible representation (irreps) of Fm3m. These modes are the primary order parameters (oops) and their number is equal to the number of irreps of T_2g and T_1g symmetry within the manifolds under consideration. Taking into account irreps up to the manifold 1=12, we have studied the rotation-rotation-translation (RRT) coupling between the oops and the lattice displacements. We have investigated the resulting lattice contraction and the change of the elastic constant c₁₁ at the phase transition. In solid C₇₀ (fcc-phase) we investigate the bilinear coupling of orientational fluctuations of T_2g symmetry to transverse acoustic lattice displacements. This coupling is the driving mechanism for the ferroelastic phase transition Fm3m → R3m. Finally we investigate the transition from the rhombohedral phase to a low temperature monoclinic phase. This transition in antiferro-rotational.     

Analysis of the temperature dependence of the heat capacity of solid tin in the vicinity of its melting temperature

Summary The experimental temperature dependence of the heat capacityC _p(T) of solid tin (Sn) in its premelting region 402.07–502.22 K was investigated and two regions with different temperature dependences ofC _p(T) were found. In the far (from the melting temperatureT _m) region 402.07–485.88 K the experimentalC _p(T) of Sn is described by the standard vacancy model. In the close region 485.88–502.22 K it is described by the formation of complicated volumetric defects in the crystalline lattice of solid Sn near itsT _m.     

Solubility of gallium in tin in the solid state

Conclusions It has been shown by X-ray diffraction and metallographic investigation that a solid solution of gallium in tin is formed when liquid gallium is placed on the surface of solid tin or when a tin-gallium alloy is produced artifically by mixing the metals in the liquid state. The solid solution grains are not etched by some reagents in the same way as the grains of tin, and the microhardness of the solid solution is 42 ± ± 8 kg/mm² compared with 12 ± 2 kg/mm² for pure tin. Calculations on 24 X-ray reflections showed that the lattice constants of the tin decreased when the solid solution was formed: Constanta decreased from 5.818 to 5.777 Å, i.e., by 0.70%, and constant c decreased from 3.183 to 3.164 Å, i.e., by 0.60%. The direction of the changes in the lattice constants agree well with the cyrstallographic and chemical data on the ionic radii of tin and gallium.In conclusion the author wishes to express his gratitude to E. D. Shchukin, A. V. Pertsov, and N. V. Pertsov for contributing to the discussion of the results and to L. L. Krapivin for help in carrying out the experiments.     

Structure and M?ssbauer studies of manganese monosulfide solid solutions MxMn1 ? xS (M = Cr, Fe)

This paper reports on the results of the synthesis and study of the diffraction patterns and M?ssbauer spectra of single crystals of homogeneous M xMn_{1 − x} S solid solutions with a cubic NaCl structure prepared by the cation substitution of 3d elements for divalent manganese ions in manganese monosulfide. It has been shown that, similarly to the hydrostatic pressure, the substitution of 3d ions with a smaller ionic radius is accompanied by the contraction of the MnS cubic cell. The calculated lattice parameters agree with the experimental data. The homogeneous region of the formation of homogeneous solid solutions is limited in composition x, which depends on the choice of a substitutional cation.     

Topological order in an exactly solvable 3D spin model

We study a 3D generalization of the toric code model introduced recently by Chamon. This is an exactly solvable spin model with six-qubit nearest-neighbor interactions on an FCC lattice whose ground space exhibits topological quantum order. The elementary excitations of this model which we call monopoles can be geometrically described as the corners of rectangular-shaped membranes. We prove that the creation of an isolated monopole separated from other monopoles by a distance R requires an operator acting on Ω(R²) qubits. Composite particles that consist of two monopoles (dipoles) and four monopoles (quadrupoles) can be described as end-points of strings. The peculiar feature of the model is that dipole-type strings are rigid, that is, such strings must be aligned with face-diagonals of the lattice. For periodic boundary conditions the ground space can encode 4g qubits where g is the greatest common divisor of the lattice dimensions. We describe a complete set of logical operators acting on the encoded qubits in terms of closed strings and closed membranes.     

Thermal expansion and thermal conductivity of CuGa<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>In<Subscript>x</Subscript>Te<Subscript>2</Subscript> solid solutions

The thermal expansion coefficients and the thermal conductivity of Bridgman-grown crystals of CuGa_1−x In_xTe₂ solid solutions are investigated. It is found that the thermal expansion coefficient varies with x linearly, while the thermal conductivity is minimal when x=0.5. The Debye temperature and the rms dynamic atomic displacements are calculated from experimental data. It is shown that the Debye temperature decreases and the rms displacements in the crystal lattice sharply increase as the In content in the solid solutions grows.     

Double structure of molten metals

Experiments show that two structures occur in solid amorphous and in molten Bi, i.e. the spherical close packing and the layer lattice structure. Here the layer lattices are neither a fragment nor a part of the Bi lattice, but they are produced from the lattice by a reduction of the interlayer distance.

This double structure is also found in the monoatomic metal melts. In the atomic distribution curves of molten In and Sn the double structure shows up as a straight atomic chain with the respective distances within the chain r_v =v×r ₁ and rv/' =v×r 1/', where r ₁ and r 1/' mean the shortest atomic distance in the spherical close packing and in the layer lattice structure. In the melts of Au, Ag, Pb and T1 as of Na and Cs, however, the spherical close packing shows up as a zig-zag chain. The straight atomic chain and the zig-zag chain are in fact imaginary, being parts of layer lattices with limited order.

In conclusion the real zig-zag chain of solid amorphous Se is considered. Even here layer lattices, composed of plane atomic chains, are found, but never single isolated atomic chains.     

Thermopower of Al1−x Six solid solutions in vicinity of lattice instability

The thermopower coefficient as a function of temperature, S(T), has been measured in nonequilibrium superconductors, such as Al_1−x Six substitutional solid solutions and Al-Si alloys on various decay stages. When aluminum is substituted with silicon, the contribution to the thermopower due to phonon-drag effects, which are dominant in pure aluminum at low temperatures, is suppressed, and low-temperature anomalies in S(T) detected in compositions near lattice instability limit are determined by the diffusion component of the thermopower. The low-temperature anomalies in the thermopower and the notable increase in the coefficient in front of the linear term in S(T) are attributed to effects of thermopower renormalization due to the electron-phonon interaction enhancement with “soft modes” in the face-centered cubic (FCC) lattice of Al_1−x Six solid solutions. The nature of these anomalies in S(T) is analyzed in terms of the Kaiser and Reizer-Sergeev models. Zh. éksp. Teor. Fiz. 113, 339–351 (January 1998)     

An NMR investigation of naphthalene nanostructures

The molecular mobility of naphthalene molecules in porous silica has been studied over the temperature range 223?K to 363?K using NMR relaxation times T ₂, T ₁ and T _1ρ. The investigations were conducted in silicas with nominal pore diameters of 4?nm, 6?nm, 10?nm, 20?nm and 50?nm. The confined solid behaved in a way that indicated it formed a dual phase system consisting of a solid core in the centre of the pores surrounded by a mobile surface layer. The core naphthalene had the same line width as the bulk. The surface layer exhibited a narrower line of a width that suggested the onset of motional narrowing. This behaviour was characteristic of a plastic crystal phase for naphthalene that does not exist in the bulk. The T ₁ and T _1ρ results were dominated by surface interactions between the confined naphthalene and the pore wall. Magnetization transfer experiments showed that enhanced relaxation occurred throughout the confined material in a time long compared to T ₂ but short compared to T ₁ and T _1ρ. Since the line shape ruled out diffusional motion through the rigid lattice naphthalene core, the magnetization transfer must have occurred via spin diffusion.     

The first principle studies of the structural and vibrational properties of solid β-HMX under compression

The structural, vibrational and electronic properties of β-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (β-HMX) crystal under high pressure up to 40 GPa have been studied using density functional theory (DFT). The pressure dependences on the cell volume, lattice constants, and molecular geometry of solid β-HMX are presented and discussed. It is found that the N–N bonds are significantly reduced under compression, which may be of importance for initial decomposition. Based on the optimized crystal structures, the vibrational frequencies for the internal and lattice modes of the β-HMX crystal at ambient and high pressures are computed, and the pressure-induced frequency shifts of these modes are discussed.     

Inelastic scattering of phonons by quadrupole defects with internal degrees of freedom

We solve the quantum mechanical problem of the inelastic scattering of phonons by a quadrupole defect in a crystal lattice for the case of solid parahydrogen whose matrix contains pair complexes of H₂ orthomolecules. By employing the pseudospin approximation for the operator of the energy of quadrupole-quadrupole interaction of the molecules in an orthopair we derive an effective Hamiltonian that describes the interaction of phonons with a pair quadrupole orthodefect in the lattice. We set up the scattering matrix and calculate the effective phonon relaxation time τ(ω, T) as a function of the frequency ω and the crystal temperature T. We also find that a pair quadrupole defect, which has a complicated system of levels, can be replaced by an effective two-level system with temperature-dependent parameters. The fact that a pair quadrupole orthocluster has internal degrees of freedom results in a resonant scattering peak near a certain critical temperature T ₀. Our estimates for H₂ yield T ₀≃ 6–7 K. Finally, we discuss the contribution of this mechanism to the low-temperature thermal conductivity of solid hydrogen. Zh. éksp. Teor. Fiz. 114, 555–569 (August 1998)     

Consequences of relativity for the hyperfine interactions — with applications to transition metals

The strong influence of relativity on the hyperfine interaction is demonstrated by non-, scalar andfully relativistic calculations for solid transition metal systems. By calculations of hyperfine fields andof the nuclear spin lattice relaxation rate of Ag in Ag _x Pt_1–x it is shown that scalar relativistic calculations, which neglect the influence of spin-orbit coupling, seem to be sufficient to account for relativistic effects in many cases. To account properly for the symmetry-breaking caused by spin-orbit coupling, which is reflected by many hyperfine interaction properties, a fully relativistic approach is demanded. The corresponding formalism in the framework of the KKR-GF (Korringa-Kohn-Rostoker-Green's function) method of band structure calculation for magnetic solids is outlined. As applications results for the hyperfine fields of pure transition metals andalloys are presented.